Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(76,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.i (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.15 | ||
Root | \(1.86824 + 0.357358i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.76 |
Dual form | 1155.2.i.c.76.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.60278i | 1.84044i | 0.391397 | + | 0.920222i | \(0.371992\pi\) | ||||
−0.391397 | + | 0.920222i | \(0.628008\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −4.77447 | −2.38723 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 2.60278 | 1.06258 | ||||||||
\(7\) | −2.60278 | + | 0.474903i | −0.983759 | + | 0.179496i | ||||
\(8\) | − | 7.22133i | − | 2.55313i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −2.60278 | −0.823072 | ||||||||
\(11\) | 3.23607 | + | 0.726543i | 0.975711 | + | 0.219061i | ||||
\(12\) | 4.77447i | 1.37827i | ||||||||
\(13\) | −6.07163 | −1.68397 | −0.841984 | − | 0.539502i | \(-0.818612\pi\) | ||||
−0.841984 | + | 0.539502i | \(0.818612\pi\) | |||||||
\(14\) | −1.23607 | − | 6.77447i | −0.330353 | − | 1.81055i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 9.24660 | 2.31165 | ||||||||
\(17\) | −4.27913 | −1.03784 | −0.518921 | − | 0.854822i | \(-0.673666\pi\) | ||||
−0.518921 | + | 0.854822i | \(0.673666\pi\) | |||||||
\(18\) | − | 2.60278i | − | 0.613481i | ||||||
\(19\) | 2.82604 | 0.648339 | 0.324169 | − | 0.945999i | \(-0.394915\pi\) | ||||
0.324169 | + | 0.945999i | \(0.394915\pi\) | |||||||
\(20\) | − | 4.77447i | − | 1.06760i | ||||||
\(21\) | 0.474903 | + | 2.60278i | 0.103632 | + | 0.567973i | ||||
\(22\) | −1.89103 | + | 8.42278i | −0.403169 | + | 1.79574i | ||||
\(23\) | 5.77447 | 1.20406 | 0.602030 | − | 0.798474i | \(-0.294359\pi\) | ||||
0.602030 | + | 0.798474i | \(0.294359\pi\) | |||||||
\(24\) | −7.22133 | −1.47405 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | − | 15.8031i | − | 3.09925i | ||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 12.4269 | − | 2.26741i | 2.34846 | − | 0.428500i | ||||
\(29\) | − | 6.49479i | − | 1.20605i | −0.797722 | − | 0.603026i | \(-0.793962\pi\) | ||
0.797722 | − | 0.603026i | \(-0.206038\pi\) | |||||||
\(30\) | 2.60278i | 0.475201i | ||||||||
\(31\) | − | 2.66550i | − | 0.478738i | −0.970929 | − | 0.239369i | \(-0.923060\pi\) | ||
0.970929 | − | 0.239369i | \(-0.0769405\pi\) | |||||||
\(32\) | 9.62422i | 1.70134i | ||||||||
\(33\) | 0.726543 | − | 3.23607i | 0.126475 | − | 0.563327i | ||||
\(34\) | − | 11.1376i | − | 1.91009i | ||||||
\(35\) | −0.474903 | − | 2.60278i | −0.0802732 | − | 0.439950i | ||||
\(36\) | 4.77447 | 0.795745 | ||||||||
\(37\) | 2.66550 | 0.438205 | 0.219103 | − | 0.975702i | \(-0.429687\pi\) | ||||
0.219103 | + | 0.975702i | \(0.429687\pi\) | |||||||
\(38\) | 7.35557i | 1.19323i | ||||||||
\(39\) | 6.07163i | 0.972240i | ||||||||
\(40\) | 7.22133 | 1.14179 | ||||||||
\(41\) | 8.37103 | 1.30733 | 0.653667 | − | 0.756782i | \(-0.273230\pi\) | ||||
0.653667 | + | 0.756782i | \(0.273230\pi\) | |||||||
\(42\) | −6.77447 | + | 1.23607i | −1.04532 | + | 0.190729i | ||||
\(43\) | − | 11.9794i | − | 1.82684i | −0.407015 | − | 0.913421i | \(-0.633430\pi\) | ||
0.407015 | − | 0.913421i | \(-0.366570\pi\) | |||||||
\(44\) | −15.4505 | − | 3.46885i | −2.32925 | − | 0.522949i | ||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 15.0297i | 2.21600i | ||||||||
\(47\) | − | 12.6655i | − | 1.84745i | −0.383053 | − | 0.923726i | \(-0.625127\pi\) | ||
0.383053 | − | 0.923726i | \(-0.374873\pi\) | |||||||
\(48\) | − | 9.24660i | − | 1.33463i | ||||||
\(49\) | 6.54893 | − | 2.47214i | 0.935562 | − | 0.353162i | ||||
\(50\) | − | 2.60278i | − | 0.368089i | ||||||
\(51\) | 4.27913i | 0.599198i | ||||||||
\(52\) | 28.9888 | 4.02003 | ||||||||
\(53\) | −13.1055 | −1.80017 | −0.900087 | − | 0.435710i | \(-0.856497\pi\) | ||||
−0.900087 | + | 0.435710i | \(0.856497\pi\) | |||||||
\(54\) | −2.60278 | −0.354194 | ||||||||
\(55\) | −0.726543 | + | 3.23607i | −0.0979670 | + | 0.436351i | ||||
\(56\) | 3.42943 | + | 18.7955i | 0.458277 | + | 2.51166i | ||||
\(57\) | − | 2.82604i | − | 0.374319i | ||||||
\(58\) | 16.9045 | 2.21967 | ||||||||
\(59\) | 4.89103i | 0.636758i | 0.947964 | + | 0.318379i | \(0.103138\pi\) | ||||
−0.947964 | + | 0.318379i | \(0.896862\pi\) | |||||||
\(60\) | −4.77447 | −0.616381 | ||||||||
\(61\) | −7.86414 | −1.00690 | −0.503450 | − | 0.864024i | \(-0.667936\pi\) | ||||
−0.503450 | + | 0.864024i | \(0.667936\pi\) | |||||||
\(62\) | 6.93771 | 0.881090 | ||||||||
\(63\) | 2.60278 | − | 0.474903i | 0.327920 | − | 0.0598321i | ||||
\(64\) | −6.55653 | −0.819566 | ||||||||
\(65\) | − | 6.07163i | − | 0.753094i | ||||||
\(66\) | 8.42278 | + | 1.89103i | 1.03677 | + | 0.232770i | ||||
\(67\) | 2.92320 | 0.357126 | 0.178563 | − | 0.983928i | \(-0.442855\pi\) | ||||
0.178563 | + | 0.983928i | \(0.442855\pi\) | |||||||
\(68\) | 20.4306 | 2.47757 | ||||||||
\(69\) | − | 5.77447i | − | 0.695164i | ||||||
\(70\) | 6.77447 | − | 1.23607i | 0.809704 | − | 0.147738i | ||||
\(71\) | −11.1376 | −1.32179 | −0.660897 | − | 0.750477i | \(-0.729824\pi\) | ||||
−0.660897 | + | 0.750477i | \(0.729824\pi\) | |||||||
\(72\) | 7.22133i | 0.851042i | ||||||||
\(73\) | −4.53482 | −0.530760 | −0.265380 | − | 0.964144i | \(-0.585497\pi\) | ||||
−0.265380 | + | 0.964144i | \(0.585497\pi\) | |||||||
\(74\) | 6.93771i | 0.806492i | ||||||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | −13.4929 | −1.54774 | ||||||||
\(77\) | −8.76781 | − | 0.354213i | −0.999185 | − | 0.0403663i | ||||
\(78\) | −15.8031 | −1.78935 | ||||||||
\(79\) | 7.42122i | 0.834952i | 0.908688 | + | 0.417476i | \(0.137085\pi\) | ||||
−0.908688 | + | 0.417476i | \(0.862915\pi\) | |||||||
\(80\) | 9.24660i | 1.03380i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 21.7879i | 2.40608i | ||||||||
\(83\) | 9.31722 | 1.02270 | 0.511349 | − | 0.859373i | \(-0.329146\pi\) | ||||
0.511349 | + | 0.859373i | \(0.329146\pi\) | |||||||
\(84\) | −2.26741 | − | 12.4269i | −0.247395 | − | 1.35588i | ||||
\(85\) | − | 4.27913i | − | 0.464137i | ||||||
\(86\) | 31.1798 | 3.36220 | ||||||||
\(87\) | −6.49479 | −0.696314 | ||||||||
\(88\) | 5.24660 | − | 23.3687i | 0.559290 | − | 2.49111i | ||||
\(89\) | 0.418895i | 0.0444028i | 0.999754 | + | 0.0222014i | \(0.00706750\pi\) | ||||
−0.999754 | + | 0.0222014i | \(0.992932\pi\) | |||||||
\(90\) | 2.60278 | 0.274357 | ||||||||
\(91\) | 15.8031 | − | 2.88344i | 1.65662 | − | 0.302266i | ||||
\(92\) | −27.5700 | −2.87437 | ||||||||
\(93\) | −2.66550 | −0.276399 | ||||||||
\(94\) | 32.9655 | 3.40013 | ||||||||
\(95\) | 2.82604i | 0.289946i | ||||||||
\(96\) | 9.62422 | 0.982268 | ||||||||
\(97\) | 2.43997i | 0.247741i | 0.992298 | + | 0.123870i | \(0.0395307\pi\) | ||||
−0.992298 | + | 0.123870i | \(0.960469\pi\) | |||||||
\(98\) | 6.43443 | + | 17.0454i | 0.649975 | + | 1.72185i | ||||
\(99\) | −3.23607 | − | 0.726543i | −0.325237 | − | 0.0730203i | ||||
\(100\) | 4.77447 | 0.477447 | ||||||||
\(101\) | 6.15537 | 0.612482 | 0.306241 | − | 0.951954i | \(-0.400929\pi\) | ||||
0.306241 | + | 0.951954i | \(0.400929\pi\) | |||||||
\(102\) | −11.1376 | −1.10279 | ||||||||
\(103\) | − | 13.1300i | − | 1.29374i | −0.762600 | − | 0.646871i | \(-0.776077\pi\) | ||
0.762600 | − | 0.646871i | \(-0.223923\pi\) | |||||||
\(104\) | 43.8453i | 4.29938i | ||||||||
\(105\) | −2.60278 | + | 0.474903i | −0.254005 | + | 0.0463458i | ||||
\(106\) | − | 34.1106i | − | 3.31312i | ||||||
\(107\) | 10.1032i | 0.976710i | 0.872645 | + | 0.488355i | \(0.162403\pi\) | ||||
−0.872645 | + | 0.488355i | \(0.837597\pi\) | |||||||
\(108\) | − | 4.77447i | − | 0.459423i | ||||||
\(109\) | 2.21566i | 0.212222i | 0.994354 | + | 0.106111i | \(0.0338398\pi\) | ||||
−0.994354 | + | 0.106111i | \(0.966160\pi\) | |||||||
\(110\) | −8.42278 | − | 1.89103i | −0.803080 | − | 0.180303i | ||||
\(111\) | − | 2.66550i | − | 0.252998i | ||||||
\(112\) | −24.0669 | + | 4.39124i | −2.27411 | + | 0.414933i | ||||
\(113\) | −6.00759 | −0.565147 | −0.282573 | − | 0.959246i | \(-0.591188\pi\) | ||||
−0.282573 | + | 0.959246i | \(0.591188\pi\) | |||||||
\(114\) | 7.35557 | 0.688912 | ||||||||
\(115\) | 5.77447i | 0.538472i | ||||||||
\(116\) | 31.0091i | 2.87913i | ||||||||
\(117\) | 6.07163 | 0.561323 | ||||||||
\(118\) | −12.7303 | −1.17192 | ||||||||
\(119\) | 11.1376 | − | 2.03217i | 1.02099 | − | 0.186289i | ||||
\(120\) | − | 7.22133i | − | 0.659214i | ||||||
\(121\) | 9.94427 | + | 4.70228i | 0.904025 | + | 0.427480i | ||||
\(122\) | − | 20.4686i | − | 1.85314i | ||||||
\(123\) | − | 8.37103i | − | 0.754790i | ||||||
\(124\) | 12.7263i | 1.14286i | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 1.23607 | + | 6.77447i | 0.110118 | + | 0.603518i | ||||
\(127\) | − | 1.01017i | − | 0.0896377i | −0.998995 | − | 0.0448188i | \(-0.985729\pi\) | ||
0.998995 | − | 0.0448188i | \(-0.0142711\pi\) | |||||||
\(128\) | 2.18323i | 0.192972i | ||||||||
\(129\) | −11.9794 | −1.05473 | ||||||||
\(130\) | 15.8031 | 1.38603 | ||||||||
\(131\) | −20.3387 | −1.77700 | −0.888502 | − | 0.458873i | \(-0.848253\pi\) | ||||
−0.888502 | + | 0.458873i | \(0.848253\pi\) | |||||||
\(132\) | −3.46885 | + | 15.4505i | −0.301925 | + | 1.34479i | ||||
\(133\) | −7.35557 | + | 1.34210i | −0.637809 | + | 0.116375i | ||||
\(134\) | 7.60845i | 0.657270i | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 30.9010i | 2.64974i | ||||||||
\(137\) | −9.63435 | −0.823118 | −0.411559 | − | 0.911383i | \(-0.635016\pi\) | ||||
−0.411559 | + | 0.911383i | \(0.635016\pi\) | |||||||
\(138\) | 15.0297 | 1.27941 | ||||||||
\(139\) | −3.08173 | −0.261389 | −0.130695 | − | 0.991423i | \(-0.541721\pi\) | ||||
−0.130695 | + | 0.991423i | \(0.541721\pi\) | |||||||
\(140\) | 2.26741 | + | 12.4269i | 0.191631 | + | 1.05026i | ||||
\(141\) | −12.6655 | −1.06663 | ||||||||
\(142\) | − | 28.9888i | − | 2.43269i | ||||||
\(143\) | −19.6482 | − | 4.41130i | −1.64307 | − | 0.368891i | ||||
\(144\) | −9.24660 | −0.770550 | ||||||||
\(145\) | 6.49479 | 0.539363 | ||||||||
\(146\) | − | 11.8031i | − | 0.976834i | ||||||
\(147\) | −2.47214 | − | 6.54893i | −0.203898 | − | 0.540147i | ||||
\(148\) | −12.7263 | −1.04610 | ||||||||
\(149\) | − | 16.8456i | − | 1.38004i | −0.723790 | − | 0.690021i | \(-0.757601\pi\) | ||
0.723790 | − | 0.690021i | \(-0.242399\pi\) | |||||||
\(150\) | −2.60278 | −0.212516 | ||||||||
\(151\) | − | 16.7907i | − | 1.36641i | −0.730227 | − | 0.683204i | \(-0.760586\pi\) | ||
0.730227 | − | 0.683204i | \(-0.239414\pi\) | |||||||
\(152\) | − | 20.4078i | − | 1.65529i | ||||||
\(153\) | 4.27913 | 0.345947 | ||||||||
\(154\) | 0.921939 | − | 22.8207i | 0.0742919 | − | 1.83894i | ||||
\(155\) | 2.66550 | 0.214098 | ||||||||
\(156\) | − | 28.9888i | − | 2.32096i | ||||||
\(157\) | − | 5.04463i | − | 0.402605i | −0.979529 | − | 0.201303i | \(-0.935483\pi\) | ||
0.979529 | − | 0.201303i | \(-0.0645174\pi\) | |||||||
\(158\) | −19.3158 | −1.53668 | ||||||||
\(159\) | 13.1055i | 1.03933i | ||||||||
\(160\) | −9.62422 | −0.760861 | ||||||||
\(161\) | −15.0297 | + | 2.74231i | −1.18450 | + | 0.216124i | ||||
\(162\) | 2.60278i | 0.204494i | ||||||||
\(163\) | −16.9045 | −1.32406 | −0.662032 | − | 0.749476i | \(-0.730306\pi\) | ||||
−0.662032 | + | 0.749476i | \(0.730306\pi\) | |||||||
\(164\) | −39.9672 | −3.12091 | ||||||||
\(165\) | 3.23607 | + | 0.726543i | 0.251928 | + | 0.0565613i | ||||
\(166\) | 24.2507i | 1.88222i | ||||||||
\(167\) | −6.32283 | −0.489275 | −0.244638 | − | 0.969615i | \(-0.578669\pi\) | ||||
−0.244638 | + | 0.969615i | \(0.578669\pi\) | |||||||
\(168\) | 18.7955 | − | 3.42943i | 1.45011 | − | 0.264586i | ||||
\(169\) | 23.8647 | 1.83575 | ||||||||
\(170\) | 11.1376 | 0.854218 | ||||||||
\(171\) | −2.82604 | −0.216113 | ||||||||
\(172\) | 57.1953i | 4.36110i | ||||||||
\(173\) | 8.78248 | 0.667719 | 0.333860 | − | 0.942623i | \(-0.391649\pi\) | ||||
0.333860 | + | 0.942623i | \(0.391649\pi\) | |||||||
\(174\) | − | 16.9045i | − | 1.28153i | ||||||
\(175\) | 2.60278 | − | 0.474903i | 0.196752 | − | 0.0358993i | ||||
\(176\) | 29.9226 | + | 6.71805i | 2.25550 | + | 0.506392i | ||||
\(177\) | 4.89103 | 0.367632 | ||||||||
\(178\) | −1.09029 | −0.0817208 | ||||||||
\(179\) | −11.1224 | −0.831331 | −0.415665 | − | 0.909518i | \(-0.636451\pi\) | ||||
−0.415665 | + | 0.909518i | \(0.636451\pi\) | |||||||
\(180\) | 4.77447i | 0.355868i | ||||||||
\(181\) | − | 8.49321i | − | 0.631295i | −0.948877 | − | 0.315648i | \(-0.897778\pi\) | ||
0.948877 | − | 0.315648i | \(-0.102222\pi\) | |||||||
\(182\) | 7.50495 | + | 41.1321i | 0.556304 | + | 3.04891i | ||||
\(183\) | 7.86414i | 0.581334i | ||||||||
\(184\) | − | 41.6993i | − | 3.07412i | ||||||
\(185\) | 2.66550i | 0.195971i | ||||||||
\(186\) | − | 6.93771i | − | 0.508697i | ||||||
\(187\) | −13.8476 | − | 3.10897i | −1.01263 | − | 0.227350i | ||||
\(188\) | 60.4710i | 4.41030i | ||||||||
\(189\) | −0.474903 | − | 2.60278i | −0.0345441 | − | 0.189324i | ||||
\(190\) | −7.35557 | −0.533629 | ||||||||
\(191\) | −25.1189 | −1.81754 | −0.908771 | − | 0.417294i | \(-0.862978\pi\) | ||||
−0.908771 | + | 0.417294i | \(0.862978\pi\) | |||||||
\(192\) | 6.55653i | 0.473177i | ||||||||
\(193\) | − | 5.20556i | − | 0.374705i | −0.982293 | − | 0.187352i | \(-0.940009\pi\) | ||
0.982293 | − | 0.187352i | \(-0.0599906\pi\) | |||||||
\(194\) | −6.35069 | −0.455953 | ||||||||
\(195\) | −6.07163 | −0.434799 | ||||||||
\(196\) | −31.2677 | + | 11.8031i | −2.23341 | + | 0.843081i | ||||
\(197\) | − | 14.1068i | − | 1.00507i | −0.864557 | − | 0.502536i | \(-0.832401\pi\) | ||
0.864557 | − | 0.502536i | \(-0.167599\pi\) | |||||||
\(198\) | 1.89103 | − | 8.42278i | 0.134390 | − | 0.598581i | ||||
\(199\) | 0.217938i | 0.0154492i | 0.999970 | + | 0.00772462i | \(0.00245885\pi\) | ||||
−0.999970 | + | 0.00772462i | \(0.997541\pi\) | |||||||
\(200\) | 7.22133i | 0.510625i | ||||||||
\(201\) | − | 2.92320i | − | 0.206187i | ||||||
\(202\) | 16.0211i | 1.12724i | ||||||||
\(203\) | 3.08439 | + | 16.9045i | 0.216482 | + | 1.18646i | ||||
\(204\) | − | 20.4306i | − | 1.43043i | ||||||
\(205\) | 8.37103i | 0.584658i | ||||||||
\(206\) | 34.1746 | 2.38106 | ||||||||
\(207\) | −5.77447 | −0.401353 | ||||||||
\(208\) | −56.1420 | −3.89275 | ||||||||
\(209\) | 9.14527 | + | 2.05324i | 0.632592 | + | 0.142026i | ||||
\(210\) | −1.23607 | − | 6.77447i | −0.0852968 | − | 0.467483i | ||||
\(211\) | 26.5392i | 1.82703i | 0.406802 | + | 0.913516i | \(0.366644\pi\) | ||||
−0.406802 | + | 0.913516i | \(0.633356\pi\) | |||||||
\(212\) | 62.5716 | 4.29744 | ||||||||
\(213\) | 11.1376i | 0.763138i | ||||||||
\(214\) | −26.2963 | −1.79758 | ||||||||
\(215\) | 11.9794 | 0.816989 | ||||||||
\(216\) | 7.22133 | 0.491349 | ||||||||
\(217\) | 1.26585 | + | 6.93771i | 0.0859317 | + | 0.470962i | ||||
\(218\) | −5.76687 | −0.390582 | ||||||||
\(219\) | 4.53482i | 0.306434i | ||||||||
\(220\) | 3.46885 | − | 15.4505i | 0.233870 | − | 1.04167i | ||||
\(221\) | 25.9813 | 1.74769 | ||||||||
\(222\) | 6.93771 | 0.465628 | ||||||||
\(223\) | 1.96783i | 0.131776i | 0.997827 | + | 0.0658878i | \(0.0209879\pi\) | ||||
−0.997827 | + | 0.0658878i | \(0.979012\pi\) | |||||||
\(224\) | −4.57057 | − | 25.0497i | −0.305384 | − | 1.67371i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | − | 15.6365i | − | 1.04012i | ||||||
\(227\) | 1.60527 | 0.106546 | 0.0532729 | − | 0.998580i | \(-0.483035\pi\) | ||||
0.0532729 | + | 0.998580i | \(0.483035\pi\) | |||||||
\(228\) | 13.4929i | 0.893586i | ||||||||
\(229\) | 9.05222i | 0.598188i | 0.954224 | + | 0.299094i | \(0.0966844\pi\) | ||||
−0.954224 | + | 0.299094i | \(0.903316\pi\) | |||||||
\(230\) | −15.0297 | −0.991027 | ||||||||
\(231\) | −0.354213 | + | 8.76781i | −0.0233055 | + | 0.576880i | ||||
\(232\) | −46.9010 | −3.07920 | ||||||||
\(233\) | − | 7.41312i | − | 0.485650i | −0.970070 | − | 0.242825i | \(-0.921926\pi\) | ||
0.970070 | − | 0.242825i | \(-0.0780741\pi\) | |||||||
\(234\) | 15.8031i | 1.03308i | ||||||||
\(235\) | 12.6655 | 0.826206 | ||||||||
\(236\) | − | 23.3521i | − | 1.52009i | ||||||
\(237\) | 7.42122 | 0.482060 | ||||||||
\(238\) | 5.28929 | + | 28.9888i | 0.342854 | + | 1.87907i | ||||
\(239\) | 7.67691i | 0.496578i | 0.968686 | + | 0.248289i | \(0.0798682\pi\) | ||||
−0.968686 | + | 0.248289i | \(0.920132\pi\) | |||||||
\(240\) | 9.24660 | 0.596866 | ||||||||
\(241\) | 13.6044 | 0.876340 | 0.438170 | − | 0.898892i | \(-0.355627\pi\) | ||||
0.438170 | + | 0.898892i | \(0.355627\pi\) | |||||||
\(242\) | −12.2390 | + | 25.8828i | −0.786753 | + | 1.66381i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 37.5471 | 2.40371 | ||||||||
\(245\) | 2.47214 | + | 6.54893i | 0.157939 | + | 0.418396i | ||||
\(246\) | 21.7879 | 1.38915 | ||||||||
\(247\) | −17.1587 | −1.09178 | ||||||||
\(248\) | −19.2484 | −1.22228 | ||||||||
\(249\) | − | 9.31722i | − | 0.590455i | ||||||
\(250\) | 2.60278 | 0.164614 | ||||||||
\(251\) | − | 21.9567i | − | 1.38590i | −0.720987 | − | 0.692948i | \(-0.756311\pi\) | ||
0.720987 | − | 0.692948i | \(-0.243689\pi\) | |||||||
\(252\) | −12.4269 | + | 2.26741i | −0.782821 | + | 0.142833i | ||||
\(253\) | 18.6866 | + | 4.19540i | 1.17481 | + | 0.263762i | ||||
\(254\) | 2.62924 | 0.164973 | ||||||||
\(255\) | −4.27913 | −0.267969 | ||||||||
\(256\) | −18.7955 | −1.17472 | ||||||||
\(257\) | − | 3.99649i | − | 0.249294i | −0.992201 | − | 0.124647i | \(-0.960220\pi\) | ||
0.992201 | − | 0.124647i | \(-0.0397799\pi\) | |||||||
\(258\) | − | 31.1798i | − | 1.94117i | ||||||
\(259\) | −6.93771 | + | 1.26585i | −0.431088 | + | 0.0786563i | ||||
\(260\) | 28.9888i | 1.79781i | ||||||||
\(261\) | 6.49479i | 0.402017i | ||||||||
\(262\) | − | 52.9373i | − | 3.27047i | ||||||
\(263\) | 10.4192i | 0.642477i | 0.946998 | + | 0.321238i | \(0.104099\pi\) | ||||
−0.946998 | + | 0.321238i | \(0.895901\pi\) | |||||||
\(264\) | −23.3687 | − | 5.24660i | −1.43824 | − | 0.322906i | ||||
\(265\) | − | 13.1055i | − | 0.805062i | ||||||
\(266\) | −3.49318 | − | 19.1449i | −0.214181 | − | 1.17385i | ||||
\(267\) | 0.418895 | 0.0256360 | ||||||||
\(268\) | −13.9567 | −0.852543 | ||||||||
\(269\) | − | 22.2279i | − | 1.35526i | −0.735403 | − | 0.677630i | \(-0.763007\pi\) | ||
0.735403 | − | 0.677630i | \(-0.236993\pi\) | |||||||
\(270\) | − | 2.60278i | − | 0.158400i | ||||||
\(271\) | −4.55819 | −0.276890 | −0.138445 | − | 0.990370i | \(-0.544210\pi\) | ||||
−0.138445 | + | 0.990370i | \(0.544210\pi\) | |||||||
\(272\) | −39.5674 | −2.39913 | ||||||||
\(273\) | −2.88344 | − | 15.8031i | −0.174514 | − | 0.956449i | ||||
\(274\) | − | 25.0761i | − | 1.51490i | ||||||
\(275\) | −3.23607 | − | 0.726543i | −0.195142 | − | 0.0438122i | ||||
\(276\) | 27.5700i | 1.65952i | ||||||||
\(277\) | − | 18.0744i | − | 1.08599i | −0.839737 | − | 0.542993i | \(-0.817291\pi\) | ||
0.839737 | − | 0.542993i | \(-0.182709\pi\) | |||||||
\(278\) | − | 8.02107i | − | 0.481072i | ||||||
\(279\) | 2.66550i | 0.159579i | ||||||||
\(280\) | −18.7955 | + | 3.42943i | −1.12325 | + | 0.204948i | ||||
\(281\) | − | 12.7654i | − | 0.761517i | −0.924674 | − | 0.380759i | \(-0.875663\pi\) | ||
0.924674 | − | 0.380759i | \(-0.124337\pi\) | |||||||
\(282\) | − | 32.9655i | − | 1.96307i | ||||||
\(283\) | −12.7384 | −0.757218 | −0.378609 | − | 0.925557i | \(-0.623597\pi\) | ||||
−0.378609 | + | 0.925557i | \(0.623597\pi\) | |||||||
\(284\) | 53.1763 | 3.15543 | ||||||||
\(285\) | 2.82604 | 0.167400 | ||||||||
\(286\) | 11.4816 | − | 51.1400i | 0.678924 | − | 3.02397i | ||||
\(287\) | −21.7879 | + | 3.97542i | −1.28610 | + | 0.234662i | ||||
\(288\) | − | 9.62422i | − | 0.567113i | ||||||
\(289\) | 1.31094 | 0.0771144 | ||||||||
\(290\) | 16.9045i | 0.992667i | ||||||||
\(291\) | 2.43997 | 0.143033 | ||||||||
\(292\) | 21.6513 | 1.26705 | ||||||||
\(293\) | 14.0114 | 0.818555 | 0.409278 | − | 0.912410i | \(-0.365781\pi\) | ||||
0.409278 | + | 0.912410i | \(0.365781\pi\) | |||||||
\(294\) | 17.0454 | − | 6.43443i | 0.994110 | − | 0.375263i | ||||
\(295\) | −4.89103 | −0.284767 | ||||||||
\(296\) | − | 19.2484i | − | 1.11879i | ||||||
\(297\) | −0.726543 | + | 3.23607i | −0.0421583 | + | 0.187776i | ||||
\(298\) | 43.8453 | 2.53989 | ||||||||
\(299\) | −35.0605 | −2.02760 | ||||||||
\(300\) | − | 4.77447i | − | 0.275654i | ||||||
\(301\) | 5.68906 | + | 31.1798i | 0.327912 | + | 1.79717i | ||||
\(302\) | 43.7025 | 2.51480 | ||||||||
\(303\) | − | 6.15537i | − | 0.353617i | ||||||
\(304\) | 26.1313 | 1.49873 | ||||||||
\(305\) | − | 7.86414i | − | 0.450299i | ||||||
\(306\) | 11.1376i | 0.636696i | ||||||||
\(307\) | −8.27920 | −0.472519 | −0.236259 | − | 0.971690i | \(-0.575922\pi\) | ||||
−0.236259 | + | 0.971690i | \(0.575922\pi\) | |||||||
\(308\) | 41.8616 | + | 1.69118i | 2.38529 | + | 0.0963638i | ||||
\(309\) | −13.1300 | −0.746942 | ||||||||
\(310\) | 6.93771i | 0.394035i | ||||||||
\(311\) | − | 11.0297i | − | 0.625436i | −0.949846 | − | 0.312718i | \(-0.898761\pi\) | ||
0.949846 | − | 0.312718i | \(-0.101239\pi\) | |||||||
\(312\) | 43.8453 | 2.48225 | ||||||||
\(313\) | 7.27776i | 0.411363i | 0.978619 | + | 0.205682i | \(0.0659411\pi\) | ||||
−0.978619 | + | 0.205682i | \(0.934059\pi\) | |||||||
\(314\) | 13.1301 | 0.740972 | ||||||||
\(315\) | 0.474903 | + | 2.60278i | 0.0267577 | + | 0.146650i | ||||
\(316\) | − | 35.4324i | − | 1.99323i | ||||||
\(317\) | 8.69007 | 0.488083 | 0.244042 | − | 0.969765i | \(-0.421527\pi\) | ||||
0.244042 | + | 0.969765i | \(0.421527\pi\) | |||||||
\(318\) | −34.1106 | −1.91283 | ||||||||
\(319\) | 4.71874 | − | 21.0176i | 0.264199 | − | 1.17676i | ||||
\(320\) | − | 6.55653i | − | 0.366521i | ||||||
\(321\) | 10.1032 | 0.563904 | ||||||||
\(322\) | −7.13763 | − | 39.1189i | −0.397765 | − | 2.18001i | ||||
\(323\) | −12.0930 | −0.672873 | ||||||||
\(324\) | −4.77447 | −0.265248 | ||||||||
\(325\) | 6.07163 | 0.336794 | ||||||||
\(326\) | − | 43.9987i | − | 2.43686i | ||||||
\(327\) | 2.21566 | 0.122526 | ||||||||
\(328\) | − | 60.4499i | − | 3.33779i | ||||||
\(329\) | 6.01488 | + | 32.9655i | 0.331611 | + | 1.81745i | ||||
\(330\) | −1.89103 | + | 8.42278i | −0.104098 | + | 0.463659i | ||||
\(331\) | 17.2380 | 0.947486 | 0.473743 | − | 0.880663i | \(-0.342903\pi\) | ||||
0.473743 | + | 0.880663i | \(0.342903\pi\) | |||||||
\(332\) | −44.4848 | −2.44142 | ||||||||
\(333\) | −2.66550 | −0.146068 | ||||||||
\(334\) | − | 16.4569i | − | 0.900484i | ||||||
\(335\) | 2.92320i | 0.159712i | ||||||||
\(336\) | 4.39124 | + | 24.0669i | 0.239562 | + | 1.31296i | ||||
\(337\) | − | 5.09846i | − | 0.277731i | −0.990311 | − | 0.138865i | \(-0.955654\pi\) | ||
0.990311 | − | 0.138865i | \(-0.0443455\pi\) | |||||||
\(338\) | 62.1147i | 3.37859i | ||||||||
\(339\) | 6.00759i | 0.326288i | ||||||||
\(340\) | 20.4306i | 1.10800i | ||||||||
\(341\) | 1.93660 | − | 8.62573i | 0.104873 | − | 0.467110i | ||||
\(342\) | − | 7.35557i | − | 0.397744i | ||||||
\(343\) | −15.8714 | + | 9.54454i | −0.856976 | + | 0.515356i | ||||
\(344\) | −86.5073 | −4.66416 | ||||||||
\(345\) | 5.77447 | 0.310887 | ||||||||
\(346\) | 22.8589i | 1.22890i | ||||||||
\(347\) | − | 4.63022i | − | 0.248563i | −0.992247 | − | 0.124282i | \(-0.960337\pi\) | ||
0.992247 | − | 0.124282i | \(-0.0396626\pi\) | |||||||
\(348\) | 31.0091 | 1.66226 | ||||||||
\(349\) | 14.2418 | 0.762347 | 0.381173 | − | 0.924504i | \(-0.375520\pi\) | ||||
0.381173 | + | 0.924504i | \(0.375520\pi\) | |||||||
\(350\) | 1.23607 | + | 6.77447i | 0.0660706 | + | 0.362111i | ||||
\(351\) | − | 6.07163i | − | 0.324080i | ||||||
\(352\) | −6.99241 | + | 31.1446i | −0.372696 | + | 1.66001i | ||||
\(353\) | − | 12.7755i | − | 0.679971i | −0.940431 | − | 0.339985i | \(-0.889578\pi\) | ||
0.940431 | − | 0.339985i | \(-0.110422\pi\) | |||||||
\(354\) | 12.7303i | 0.676607i | ||||||||
\(355\) | − | 11.1376i | − | 0.591124i | ||||||
\(356\) | − | 2.00000i | − | 0.106000i | ||||||
\(357\) | −2.03217 | − | 11.1376i | −0.107554 | − | 0.589466i | ||||
\(358\) | − | 28.9493i | − | 1.53002i | ||||||
\(359\) | − | 16.6836i | − | 0.880527i | −0.897869 | − | 0.440263i | \(-0.854885\pi\) | ||
0.897869 | − | 0.440263i | \(-0.145115\pi\) | |||||||
\(360\) | −7.22133 | −0.380598 | ||||||||
\(361\) | −11.0135 | −0.579657 | ||||||||
\(362\) | 22.1060 | 1.16186 | ||||||||
\(363\) | 4.70228 | − | 9.94427i | 0.246806 | − | 0.521939i | ||||
\(364\) | −75.4515 | + | 13.7669i | −3.95474 | + | 0.721580i | ||||
\(365\) | − | 4.53482i | − | 0.237363i | ||||||
\(366\) | −20.4686 | −1.06991 | ||||||||
\(367\) | 28.2279i | 1.47348i | 0.676174 | + | 0.736742i | \(0.263637\pi\) | ||||
−0.676174 | + | 0.736742i | \(0.736363\pi\) | |||||||
\(368\) | 53.3942 | 2.78337 | ||||||||
\(369\) | −8.37103 | −0.435778 | ||||||||
\(370\) | −6.93771 | −0.360674 | ||||||||
\(371\) | 34.1106 | − | 6.22382i | 1.77094 | − | 0.323125i | ||||
\(372\) | 12.7263 | 0.659830 | ||||||||
\(373\) | 9.90424i | 0.512822i | 0.966568 | + | 0.256411i | \(0.0825400\pi\) | ||||
−0.966568 | + | 0.256411i | \(0.917460\pi\) | |||||||
\(374\) | 8.09196 | − | 36.0421i | 0.418426 | − | 1.86369i | ||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −91.4617 | −4.71678 | ||||||||
\(377\) | 39.4340i | 2.03095i | ||||||||
\(378\) | 6.77447 | − | 1.23607i | 0.348441 | − | 0.0635765i | ||||
\(379\) | 25.7464 | 1.32250 | 0.661251 | − | 0.750164i | \(-0.270026\pi\) | ||||
0.661251 | + | 0.750164i | \(0.270026\pi\) | |||||||
\(380\) | − | 13.4929i | − | 0.692169i | ||||||
\(381\) | −1.01017 | −0.0517523 | ||||||||
\(382\) | − | 65.3791i | − | 3.34509i | ||||||
\(383\) | 10.5119i | 0.537133i | 0.963261 | + | 0.268567i | \(0.0865499\pi\) | ||||
−0.963261 | + | 0.268567i | \(0.913450\pi\) | |||||||
\(384\) | 2.18323 | 0.111413 | ||||||||
\(385\) | 0.354213 | − | 8.76781i | 0.0180524 | − | 0.446849i | ||||
\(386\) | 13.5489 | 0.689623 | ||||||||
\(387\) | 11.9794i | 0.608948i | ||||||||
\(388\) | − | 11.6495i | − | 0.591416i | ||||||
\(389\) | 17.4410 | 0.884293 | 0.442146 | − | 0.896943i | \(-0.354217\pi\) | ||||
0.442146 | + | 0.896943i | \(0.354217\pi\) | |||||||
\(390\) | − | 15.8031i | − | 0.800223i | ||||||
\(391\) | −24.7097 | −1.24962 | ||||||||
\(392\) | −17.8521 | − | 47.2920i | −0.901668 | − | 2.38861i | ||||
\(393\) | 20.3387i | 1.02595i | ||||||||
\(394\) | 36.7170 | 1.84978 | ||||||||
\(395\) | −7.42122 | −0.373402 | ||||||||
\(396\) | 15.4505 | + | 3.46885i | 0.776417 | + | 0.174316i | ||||
\(397\) | 12.0059i | 0.602558i | 0.953536 | + | 0.301279i | \(0.0974135\pi\) | ||||
−0.953536 | + | 0.301279i | \(0.902586\pi\) | |||||||
\(398\) | −0.567246 | −0.0284335 | ||||||||
\(399\) | 1.34210 | + | 7.35557i | 0.0671889 | + | 0.368239i | ||||
\(400\) | −9.24660 | −0.462330 | ||||||||
\(401\) | −14.5860 | −0.728388 | −0.364194 | − | 0.931323i | \(-0.618656\pi\) | ||||
−0.364194 | + | 0.931323i | \(0.618656\pi\) | |||||||
\(402\) | 7.60845 | 0.379475 | ||||||||
\(403\) | 16.1839i | 0.806179i | ||||||||
\(404\) | −29.3886 | −1.46214 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | −43.9987 | + | 8.02800i | −2.18362 | + | 0.398423i | ||||
\(407\) | 8.62573 | + | 1.93660i | 0.427562 | + | 0.0959936i | ||||
\(408\) | 30.9010 | 1.52983 | ||||||||
\(409\) | 8.50150 | 0.420372 | 0.210186 | − | 0.977661i | \(-0.432593\pi\) | ||||
0.210186 | + | 0.977661i | \(0.432593\pi\) | |||||||
\(410\) | −21.7879 | −1.07603 | ||||||||
\(411\) | 9.63435i | 0.475227i | ||||||||
\(412\) | 62.6889i | 3.08846i | ||||||||
\(413\) | −2.32276 | − | 12.7303i | −0.114296 | − | 0.626416i | ||||
\(414\) | − | 15.0297i | − | 0.738668i | ||||||
\(415\) | 9.31722i | 0.457365i | ||||||||
\(416\) | − | 58.4347i | − | 2.86500i | ||||||
\(417\) | 3.08173i | 0.150913i | ||||||||
\(418\) | −5.34414 | + | 23.8031i | −0.261390 | + | 1.16425i | ||||
\(419\) | 24.4400i | 1.19397i | 0.802252 | + | 0.596985i | \(0.203635\pi\) | ||||
−0.802252 | + | 0.596985i | \(0.796365\pi\) | |||||||
\(420\) | 12.4269 | − | 2.26741i | 0.606370 | − | 0.110638i | ||||
\(421\) | −22.8513 | −1.11370 | −0.556851 | − | 0.830612i | \(-0.687991\pi\) | ||||
−0.556851 | + | 0.830612i | \(0.687991\pi\) | |||||||
\(422\) | −69.0757 | −3.36255 | ||||||||
\(423\) | 12.6655i | 0.615818i | ||||||||
\(424\) | 94.6389i | 4.59607i | ||||||||
\(425\) | 4.27913 | 0.207568 | ||||||||
\(426\) | −28.9888 | −1.40451 | ||||||||
\(427\) | 20.4686 | − | 3.73470i | 0.990546 | − | 0.180735i | ||||
\(428\) | − | 48.2373i | − | 2.33164i | ||||||
\(429\) | −4.41130 | + | 19.6482i | −0.212980 | + | 0.948625i | ||||
\(430\) | 31.1798i | 1.50362i | ||||||||
\(431\) | − | 23.7265i | − | 1.14287i | −0.820649 | − | 0.571433i | \(-0.806388\pi\) | ||
0.820649 | − | 0.571433i | \(-0.193612\pi\) | |||||||
\(432\) | 9.24660i | 0.444877i | ||||||||
\(433\) | 28.1276i | 1.35172i | 0.737028 | + | 0.675862i | \(0.236228\pi\) | ||||
−0.737028 | + | 0.675862i | \(0.763772\pi\) | |||||||
\(434\) | −18.0573 | + | 3.29474i | −0.866780 | + | 0.158152i | ||||
\(435\) | − | 6.49479i | − | 0.311401i | ||||||
\(436\) | − | 10.5786i | − | 0.506623i | ||||||
\(437\) | 16.3189 | 0.780639 | ||||||||
\(438\) | −11.8031 | −0.563975 | ||||||||
\(439\) | 16.7754 | 0.800648 | 0.400324 | − | 0.916374i | \(-0.368898\pi\) | ||||
0.400324 | + | 0.916374i | \(0.368898\pi\) | |||||||
\(440\) | 23.3687 | + | 5.24660i | 1.11406 | + | 0.250122i | ||||
\(441\) | −6.54893 | + | 2.47214i | −0.311854 | + | 0.117721i | ||||
\(442\) | 67.6236i | 3.21653i | ||||||||
\(443\) | 11.1985 | 0.532055 | 0.266028 | − | 0.963965i | \(-0.414289\pi\) | ||||
0.266028 | + | 0.963965i | \(0.414289\pi\) | |||||||
\(444\) | 12.7263i | 0.603965i | ||||||||
\(445\) | −0.418895 | −0.0198575 | ||||||||
\(446\) | −5.12183 | −0.242526 | ||||||||
\(447\) | −16.8456 | −0.796767 | ||||||||
\(448\) | 17.0652 | − | 3.11371i | 0.806255 | − | 0.147109i | ||||
\(449\) | 7.48810 | 0.353385 | 0.176693 | − | 0.984266i | \(-0.443460\pi\) | ||||
0.176693 | + | 0.984266i | \(0.443460\pi\) | |||||||
\(450\) | 2.60278i | 0.122696i | ||||||||
\(451\) | 27.0892 | + | 6.08191i | 1.27558 | + | 0.286386i | ||||
\(452\) | 28.6831 | 1.34914 | ||||||||
\(453\) | −16.7907 | −0.788896 | ||||||||
\(454\) | 4.17817i | 0.196091i | ||||||||
\(455\) | 2.88344 | + | 15.8031i | 0.135178 | + | 0.740862i | ||||
\(456\) | −20.4078 | −0.955683 | ||||||||
\(457\) | 35.4188i | 1.65682i | 0.560122 | + | 0.828410i | \(0.310754\pi\) | ||||
−0.560122 | + | 0.828410i | \(0.689246\pi\) | |||||||
\(458\) | −23.5609 | −1.10093 | ||||||||
\(459\) | − | 4.27913i | − | 0.199733i | ||||||
\(460\) | − | 27.5700i | − | 1.28546i | ||||||
\(461\) | −3.80732 | −0.177324 | −0.0886622 | − | 0.996062i | \(-0.528259\pi\) | ||||
−0.0886622 | + | 0.996062i | \(0.528259\pi\) | |||||||
\(462\) | −22.8207 | − | 0.921939i | −1.06171 | − | 0.0428925i | ||||
\(463\) | −19.4164 | −0.902357 | −0.451178 | − | 0.892434i | \(-0.648996\pi\) | ||||
−0.451178 | + | 0.892434i | \(0.648996\pi\) | |||||||
\(464\) | − | 60.0547i | − | 2.78797i | ||||||
\(465\) | − | 2.66550i | − | 0.123610i | ||||||
\(466\) | 19.2947 | 0.893811 | ||||||||
\(467\) | 31.1400i | 1.44099i | 0.693461 | + | 0.720494i | \(0.256085\pi\) | ||||
−0.693461 | + | 0.720494i | \(0.743915\pi\) | |||||||
\(468\) | −28.9888 | −1.34001 | ||||||||
\(469\) | −7.60845 | + | 1.38824i | −0.351326 | + | 0.0641028i | ||||
\(470\) | 32.9655i | 1.52059i | ||||||||
\(471\) | −5.04463 | −0.232444 | ||||||||
\(472\) | 35.3197 | 1.62572 | ||||||||
\(473\) | 8.70355 | − | 38.7662i | 0.400190 | − | 1.78247i | ||||
\(474\) | 19.3158i | 0.887204i | ||||||||
\(475\) | −2.82604 | −0.129668 | ||||||||
\(476\) | −53.1763 | + | 9.70253i | −2.43733 | + | 0.444715i | ||||
\(477\) | 13.1055 | 0.600058 | ||||||||
\(478\) | −19.9813 | −0.913924 | ||||||||
\(479\) | −41.3914 | −1.89122 | −0.945610 | − | 0.325302i | \(-0.894534\pi\) | ||||
−0.945610 | + | 0.325302i | \(0.894534\pi\) | |||||||
\(480\) | 9.62422i | 0.439284i | ||||||||
\(481\) | −16.1839 | −0.737924 | ||||||||
\(482\) | 35.4094i | 1.61285i | ||||||||
\(483\) | 2.74231 | + | 15.0297i | 0.124779 | + | 0.683874i | ||||
\(484\) | −47.4786 | − | 22.4509i | −2.15812 | − | 1.02050i | ||||
\(485\) | −2.43997 | −0.110793 | ||||||||
\(486\) | 2.60278 | 0.118065 | ||||||||
\(487\) | 31.4585 | 1.42552 | 0.712761 | − | 0.701407i | \(-0.247444\pi\) | ||||
0.712761 | + | 0.701407i | \(0.247444\pi\) | |||||||
\(488\) | 56.7895i | 2.57074i | ||||||||
\(489\) | 16.9045i | 0.764448i | ||||||||
\(490\) | −17.0454 | + | 6.43443i | −0.770035 | + | 0.290678i | ||||
\(491\) | − | 14.2888i | − | 0.644845i | −0.946596 | − | 0.322422i | \(-0.895503\pi\) | ||
0.946596 | − | 0.322422i | \(-0.104497\pi\) | |||||||
\(492\) | 39.9672i | 1.80186i | ||||||||
\(493\) | 27.7920i | 1.25169i | ||||||||
\(494\) | − | 44.6603i | − | 2.00936i | ||||||
\(495\) | 0.726543 | − | 3.23607i | 0.0326557 | − | 0.145450i | ||||
\(496\) | − | 24.6468i | − | 1.10667i | ||||||
\(497\) | 28.9888 | − | 5.28929i | 1.30033 | − | 0.237257i | ||||
\(498\) | 24.2507 | 1.08670 | ||||||||
\(499\) | 16.9729 | 0.759813 | 0.379907 | − | 0.925025i | \(-0.375956\pi\) | ||||
0.379907 | + | 0.925025i | \(0.375956\pi\) | |||||||
\(500\) | 4.77447i | 0.213521i | ||||||||
\(501\) | 6.32283i | 0.282483i | ||||||||
\(502\) | 57.1486 | 2.55066 | ||||||||
\(503\) | −24.3271 | −1.08469 | −0.542347 | − | 0.840155i | \(-0.682464\pi\) | ||||
−0.542347 | + | 0.840155i | \(0.682464\pi\) | |||||||
\(504\) | −3.42943 | − | 18.7955i | −0.152759 | − | 0.837220i | ||||
\(505\) | 6.15537i | 0.273910i | ||||||||
\(506\) | −10.9197 | + | 48.6370i | −0.485440 | + | 2.16218i | ||||
\(507\) | − | 23.8647i | − | 1.05987i | ||||||
\(508\) | 4.82300i | 0.213986i | ||||||||
\(509\) | − | 42.7211i | − | 1.89358i | −0.321852 | − | 0.946790i | \(-0.604305\pi\) | ||
0.321852 | − | 0.946790i | \(-0.395695\pi\) | |||||||
\(510\) | − | 11.1376i | − | 0.493183i | ||||||
\(511\) | 11.8031 | − | 2.15360i | 0.522140 | − | 0.0952695i | ||||
\(512\) | − | 44.5542i | − | 1.96904i | ||||||
\(513\) | 2.82604i | 0.124773i | ||||||||
\(514\) | 10.4020 | 0.458812 | ||||||||
\(515\) | 13.1300 | 0.578579 | ||||||||
\(516\) | 57.1953 | 2.51788 | ||||||||
\(517\) | 9.20202 | − | 40.9864i | 0.404705 | − | 1.80258i | ||||
\(518\) | −3.29474 | − | 18.0573i | −0.144762 | − | 0.793394i | ||||
\(519\) | − | 8.78248i | − | 0.385508i | ||||||
\(520\) | −43.8453 | −1.92274 | ||||||||
\(521\) | 4.33936i | 0.190111i | 0.995472 | + | 0.0950555i | \(0.0303029\pi\) | ||||
−0.995472 | + | 0.0950555i | \(0.969697\pi\) | |||||||
\(522\) | −16.9045 | −0.739890 | ||||||||
\(523\) | 9.34869 | 0.408790 | 0.204395 | − | 0.978889i | \(-0.434477\pi\) | ||||
0.204395 | + | 0.978889i | \(0.434477\pi\) | |||||||
\(524\) | 97.1066 | 4.24212 | ||||||||
\(525\) | −0.474903 | − | 2.60278i | −0.0207265 | − | 0.113595i | ||||
\(526\) | −27.1189 | −1.18244 | ||||||||
\(527\) | 11.4060i | 0.496854i | ||||||||
\(528\) | 6.71805 | − | 29.9226i | 0.292366 | − | 1.30222i | ||||
\(529\) | 10.3445 | 0.449760 | ||||||||
\(530\) | 34.1106 | 1.48167 | ||||||||
\(531\) | − | 4.89103i | − | 0.212253i | ||||||
\(532\) | 35.1189 | − | 6.40779i | 1.52260 | − | 0.277813i | ||||
\(533\) | −50.8258 | −2.20151 | ||||||||
\(534\) | 1.09029i | 0.0471815i | ||||||||
\(535\) | −10.1032 | −0.436798 | ||||||||
\(536\) | − | 21.1094i | − | 0.911787i | ||||||
\(537\) | 11.1224i | 0.479969i | ||||||||
\(538\) | 57.8544 | 2.49428 | ||||||||
\(539\) | 22.9889 | − | 3.24192i | 0.990202 | − | 0.139639i | ||||
\(540\) | 4.77447 | 0.205460 | ||||||||
\(541\) | 26.1745i | 1.12533i | 0.826685 | + | 0.562664i | \(0.190224\pi\) | ||||
−0.826685 | + | 0.562664i | \(0.809776\pi\) | |||||||
\(542\) | − | 11.8640i | − | 0.509601i | ||||||
\(543\) | −8.49321 | −0.364478 | ||||||||
\(544\) | − | 41.1833i | − | 1.76572i | ||||||
\(545\) | −2.21566 | −0.0949084 | ||||||||
\(546\) | 41.1321 | − | 7.50495i | 1.76029 | − | 0.321182i | ||||
\(547\) | − | 7.28713i | − | 0.311575i | −0.987791 | − | 0.155788i | \(-0.950208\pi\) | ||
0.987791 | − | 0.155788i | \(-0.0497916\pi\) | |||||||
\(548\) | 45.9989 | 1.96497 | ||||||||
\(549\) | 7.86414 | 0.335633 | ||||||||
\(550\) | 1.89103 | − | 8.42278i | 0.0806338 | − | 0.359148i | ||||
\(551\) | − | 18.3546i | − | 0.781930i | ||||||
\(552\) | −41.6993 | −1.77484 | ||||||||
\(553\) | −3.52436 | − | 19.3158i | −0.149871 | − | 0.821392i | ||||
\(554\) | 47.0437 | 1.99870 | ||||||||
\(555\) | 2.66550 | 0.113144 | ||||||||
\(556\) | 14.7136 | 0.623997 | ||||||||
\(557\) | 9.67553i | 0.409965i | 0.978766 | + | 0.204983i | \(0.0657138\pi\) | ||||
−0.978766 | + | 0.204983i | \(0.934286\pi\) | |||||||
\(558\) | −6.93771 | −0.293697 | ||||||||
\(559\) | 72.7346i | 3.07635i | ||||||||
\(560\) | −4.39124 | − | 24.0669i | −0.185564 | − | 1.01701i | ||||
\(561\) | −3.10897 | + | 13.8476i | −0.131261 | + | 0.584644i | ||||
\(562\) | 33.2254 | 1.40153 | ||||||||
\(563\) | 3.97478 | 0.167517 | 0.0837586 | − | 0.996486i | \(-0.473308\pi\) | ||||
0.0837586 | + | 0.996486i | \(0.473308\pi\) | |||||||
\(564\) | 60.4710 | 2.54629 | ||||||||
\(565\) | − | 6.00759i | − | 0.252741i | ||||||
\(566\) | − | 33.1552i | − | 1.39362i | ||||||
\(567\) | −2.60278 | + | 0.474903i | −0.109307 | + | 0.0199440i | ||||
\(568\) | 80.4285i | 3.37471i | ||||||||
\(569\) | − | 19.1962i | − | 0.804746i | −0.915476 | − | 0.402373i | \(-0.868186\pi\) | ||
0.915476 | − | 0.402373i | \(-0.131814\pi\) | |||||||
\(570\) | 7.35557i | 0.308091i | ||||||||
\(571\) | 17.4974i | 0.732244i | 0.930567 | + | 0.366122i | \(0.119315\pi\) | ||||
−0.930567 | + | 0.366122i | \(0.880685\pi\) | |||||||
\(572\) | 93.8098 | + | 21.0616i | 3.92238 | + | 0.880630i | ||||
\(573\) | 25.1189i | 1.04936i | ||||||||
\(574\) | −10.3472 | − | 56.7092i | −0.431882 | − | 2.36700i | ||||
\(575\) | −5.77447 | −0.240812 | ||||||||
\(576\) | 6.55653 | 0.273189 | ||||||||
\(577\) | − | 25.7540i | − | 1.07215i | −0.844170 | − | 0.536076i | \(-0.819906\pi\) | ||
0.844170 | − | 0.536076i | \(-0.180094\pi\) | |||||||
\(578\) | 3.41210i | 0.141925i | ||||||||
\(579\) | −5.20556 | −0.216336 | ||||||||
\(580\) | −31.0091 | −1.28758 | ||||||||
\(581\) | −24.2507 | + | 4.42478i | −1.00609 | + | 0.183571i | ||||
\(582\) | 6.35069i | 0.263245i | ||||||||
\(583\) | −42.4102 | − | 9.52168i | −1.75645 | − | 0.394348i | ||||
\(584\) | 32.7474i | 1.35510i | ||||||||
\(585\) | 6.07163i | 0.251031i | ||||||||
\(586\) | 36.4686i | 1.50651i | ||||||||
\(587\) | 30.8343i | 1.27267i | 0.771414 | + | 0.636334i | \(0.219550\pi\) | ||||
−0.771414 | + | 0.636334i | \(0.780450\pi\) | |||||||
\(588\) | 11.8031 | + | 31.2677i | 0.486753 | + | 1.28946i | ||||
\(589\) | − | 7.53281i | − | 0.310384i | ||||||
\(590\) | − | 12.7303i | − | 0.524097i | ||||||
\(591\) | −14.1068 | −0.580278 | ||||||||
\(592\) | 24.6468 | 1.01298 | ||||||||
\(593\) | 11.6886 | 0.479995 | 0.239998 | − | 0.970773i | \(-0.422853\pi\) | ||||
0.239998 | + | 0.970773i | \(0.422853\pi\) | |||||||
\(594\) | −8.42278 | − | 1.89103i | −0.345591 | − | 0.0775899i | ||||
\(595\) | 2.03217 | + | 11.1376i | 0.0833109 | + | 0.456598i | ||||
\(596\) | 80.4285i | 3.29448i | ||||||||
\(597\) | 0.217938 | 0.00891962 | ||||||||
\(598\) | − | 91.2547i | − | 3.73168i | ||||||
\(599\) | 23.7879 | 0.971949 | 0.485975 | − | 0.873973i | \(-0.338465\pi\) | ||||
0.485975 | + | 0.873973i | \(0.338465\pi\) | |||||||
\(600\) | 7.22133 | 0.294810 | ||||||||
\(601\) | 27.3449 | 1.11542 | 0.557711 | − | 0.830035i | \(-0.311680\pi\) | ||||
0.557711 | + | 0.830035i | \(0.311680\pi\) | |||||||
\(602\) | −81.1541 | + | 14.8074i | −3.30759 | + | 0.603503i | ||||
\(603\) | −2.92320 | −0.119042 | ||||||||
\(604\) | 80.1667i | 3.26194i | ||||||||
\(605\) | −4.70228 | + | 9.94427i | −0.191175 | + | 0.404292i | ||||
\(606\) | 16.0211 | 0.650812 | ||||||||
\(607\) | 35.8698 | 1.45591 | 0.727955 | − | 0.685625i | \(-0.240471\pi\) | ||||
0.727955 | + | 0.685625i | \(0.240471\pi\) | |||||||
\(608\) | 27.1985i | 1.10304i | ||||||||
\(609\) | 16.9045 | − | 3.08439i | 0.685005 | − | 0.124986i | ||||
\(610\) | 20.4686 | 0.828751 | ||||||||
\(611\) | 76.9003i | 3.11105i | ||||||||
\(612\) | −20.4306 | −0.825856 | ||||||||
\(613\) | − | 30.6661i | − | 1.23859i | −0.785157 | − | 0.619297i | \(-0.787418\pi\) | ||
0.785157 | − | 0.619297i | \(-0.212582\pi\) | |||||||
\(614\) | − | 21.5489i | − | 0.869644i | ||||||
\(615\) | 8.37103 | 0.337552 | ||||||||
\(616\) | −2.55789 | + | 63.3153i | −0.103060 | + | 2.55104i | ||||
\(617\) | −12.1325 | −0.488437 | −0.244219 | − | 0.969720i | \(-0.578531\pi\) | ||||
−0.244219 | + | 0.969720i | \(0.578531\pi\) | |||||||
\(618\) | − | 34.1746i | − | 1.37470i | ||||||
\(619\) | 14.1708i | 0.569573i | 0.958591 | + | 0.284787i | \(0.0919228\pi\) | ||||
−0.958591 | + | 0.284787i | \(0.908077\pi\) | |||||||
\(620\) | −12.7263 | −0.511102 | ||||||||
\(621\) | 5.77447i | 0.231721i | ||||||||
\(622\) | 28.7078 | 1.15108 | ||||||||
\(623\) | −0.198934 | − | 1.09029i | −0.00797014 | − | 0.0436816i | ||||
\(624\) | 56.1420i | 2.24748i | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −18.9424 | −0.757091 | ||||||||
\(627\) | 2.05324 | − | 9.14527i | 0.0819985 | − | 0.365227i | ||||
\(628\) | 24.0854i | 0.961113i | ||||||||
\(629\) | −11.4060 | −0.454787 | ||||||||
\(630\) | −6.77447 | + | 1.23607i | −0.269901 | + | 0.0492461i | ||||
\(631\) | −21.9815 | −0.875072 | −0.437536 | − | 0.899201i | \(-0.644149\pi\) | ||||
−0.437536 | + | 0.899201i | \(0.644149\pi\) | |||||||
\(632\) | 53.5911 | 2.13174 | ||||||||
\(633\) | 26.5392 | 1.05484 | ||||||||
\(634\) | 22.6184i | 0.898290i | ||||||||
\(635\) | 1.01017 | 0.0400872 | ||||||||
\(636\) | − | 62.5716i | − | 2.48113i | ||||||
\(637\) | −39.7627 | + | 15.0099i | −1.57546 | + | 0.594714i | ||||
\(638\) | 54.7041 | + | 12.2818i | 2.16576 | + | 0.486243i | ||||
\(639\) | 11.1376 | 0.440598 | ||||||||
\(640\) | −2.18323 | −0.0862999 | ||||||||
\(641\) | −31.3462 | −1.23810 | −0.619050 | − | 0.785352i | \(-0.712482\pi\) | ||||
−0.619050 | + | 0.785352i | \(0.712482\pi\) | |||||||
\(642\) | 26.2963i | 1.03783i | ||||||||
\(643\) | − | 33.2517i | − | 1.31132i | −0.755057 | − | 0.655660i | \(-0.772391\pi\) | ||
0.755057 | − | 0.655660i | \(-0.227609\pi\) | |||||||
\(644\) | 71.7587 | − | 13.0931i | 2.82769 | − | 0.515939i | ||||
\(645\) | − | 11.9794i | − | 0.471689i | ||||||
\(646\) | − | 31.4754i | − | 1.23838i | ||||||
\(647\) | 37.8242i | 1.48702i | 0.668723 | + | 0.743511i | \(0.266841\pi\) | ||||
−0.668723 | + | 0.743511i | \(0.733159\pi\) | |||||||
\(648\) | − | 7.22133i | − | 0.283681i | ||||||
\(649\) | −3.55354 | + | 15.8277i | −0.139489 | + | 0.621292i | ||||
\(650\) | 15.8031i | 0.619850i | ||||||||
\(651\) | 6.93771 | − | 1.26585i | 0.271910 | − | 0.0496127i | ||||
\(652\) | 80.7100 | 3.16085 | ||||||||
\(653\) | −36.1612 | −1.41510 | −0.707548 | − | 0.706665i | \(-0.750199\pi\) | ||||
−0.707548 | + | 0.706665i | \(0.750199\pi\) | |||||||
\(654\) | 5.76687i | 0.225503i | ||||||||
\(655\) | − | 20.3387i | − | 0.794700i | ||||||
\(656\) | 77.4036 | 3.02210 | ||||||||
\(657\) | 4.53482 | 0.176920 | ||||||||
\(658\) | −85.8020 | + | 15.6554i | −3.34491 | + | 0.610312i | ||||
\(659\) | − | 0.553632i | − | 0.0215665i | −0.999942 | − | 0.0107832i | \(-0.996568\pi\) | ||
0.999942 | − | 0.0107832i | \(-0.00343248\pi\) | |||||||
\(660\) | −15.4505 | − | 3.46885i | −0.601410 | − | 0.135025i | ||||
\(661\) | 7.29711i | 0.283825i | 0.989879 | + | 0.141912i | \(0.0453251\pi\) | ||||
−0.989879 | + | 0.141912i | \(0.954675\pi\) | |||||||
\(662\) | 44.8667i | 1.74379i | ||||||||
\(663\) | − | 25.9813i | − | 1.00903i | ||||||
\(664\) | − | 67.2828i | − | 2.61108i | ||||||
\(665\) | −1.34210 | − | 7.35557i | −0.0520443 | − | 0.285237i | ||||
\(666\) | − | 6.93771i | − | 0.268831i | ||||||
\(667\) | − | 37.5039i | − | 1.45216i | ||||||
\(668\) | 30.1882 | 1.16801 | ||||||||
\(669\) | 1.96783 | 0.0760807 | ||||||||
\(670\) | −7.60845 | −0.293940 | ||||||||
\(671\) | −25.4489 | − | 5.71363i | −0.982444 | − | 0.220572i | ||||
\(672\) | −25.0497 | + | 4.57057i | −0.966315 | + | 0.176314i | ||||
\(673\) | − | 8.61671i | − | 0.332150i | −0.986113 | − | 0.166075i | \(-0.946891\pi\) | ||
0.986113 | − | 0.166075i | \(-0.0531093\pi\) | |||||||
\(674\) | 13.2702 | 0.511147 | ||||||||
\(675\) | − | 1.00000i | − | 0.0384900i | ||||||
\(676\) | −113.941 | −4.38236 | ||||||||
\(677\) | −14.1483 | −0.543764 | −0.271882 | − | 0.962331i | \(-0.587646\pi\) | ||||
−0.271882 | + | 0.962331i | \(0.587646\pi\) | |||||||
\(678\) | −15.6365 | −0.600514 | ||||||||
\(679\) | −1.15875 | − | 6.35069i | −0.0444686 | − | 0.243717i | ||||
\(680\) | −30.9010 | −1.18500 | ||||||||
\(681\) | − | 1.60527i | − | 0.0615142i | ||||||
\(682\) | 22.4509 | + | 5.04054i | 0.859689 | + | 0.193012i | ||||
\(683\) | −40.0141 | −1.53110 | −0.765548 | − | 0.643379i | \(-0.777532\pi\) | ||||
−0.765548 | + | 0.643379i | \(0.777532\pi\) | |||||||
\(684\) | 13.4929 | 0.515912 | ||||||||
\(685\) | − | 9.63435i | − | 0.368109i | ||||||
\(686\) | −24.8423 | − | 41.3098i | −0.948485 | − | 1.57722i | ||||
\(687\) | 9.05222 | 0.345364 | ||||||||
\(688\) | − | 110.769i | − | 4.22302i | ||||||
\(689\) | 79.5716 | 3.03144 | ||||||||
\(690\) | 15.0297i | 0.572170i | ||||||||
\(691\) | 0.111456i | 0.00423999i | 0.999998 | + | 0.00212000i | \(0.000674816\pi\) | ||||
−0.999998 | + | 0.00212000i | \(0.999325\pi\) | |||||||
\(692\) | −41.9316 | −1.59400 | ||||||||
\(693\) | 8.76781 | + | 0.354213i | 0.333062 | + | 0.0134554i | ||||
\(694\) | 12.0514 | 0.457467 | ||||||||
\(695\) | − | 3.08173i | − | 0.116897i | ||||||
\(696\) | 46.9010i | 1.77778i | ||||||||
\(697\) | −35.8207 | −1.35681 | ||||||||
\(698\) | 37.0683i | 1.40306i | ||||||||
\(699\) | −7.41312 | −0.280390 | ||||||||
\(700\) | −12.4269 | + | 2.26741i | −0.469692 | + | 0.0857000i | ||||
\(701\) | − | 2.90978i | − | 0.109901i | −0.998489 | − | 0.0549504i | \(-0.982500\pi\) | ||
0.998489 | − | 0.0549504i | \(-0.0175001\pi\) | |||||||
\(702\) | 15.8031 | 0.596451 | ||||||||
\(703\) | 7.53281 | 0.284105 | ||||||||
\(704\) | −21.2174 | − | 4.76360i | −0.799660 | − | 0.179535i | ||||
\(705\) | − | 12.6655i | − | 0.477010i | ||||||
\(706\) | 33.2518 | 1.25145 | ||||||||
\(707\) | −16.0211 | + | 2.92320i | −0.602534 | + | 0.109938i | ||||
\(708\) | −23.3521 | −0.877624 | ||||||||
\(709\) | 26.1351 | 0.981526 | 0.490763 | − | 0.871293i | \(-0.336718\pi\) | ||||
0.490763 | + | 0.871293i | \(0.336718\pi\) | |||||||
\(710\) | 28.9888 | 1.08793 | ||||||||
\(711\) | − | 7.42122i | − | 0.278317i | ||||||
\(712\) | 3.02498 | 0.113366 | ||||||||
\(713\) | − | 15.3918i | − | 0.576429i | ||||||
\(714\) | 28.9888 | − | 5.28929i | 1.08488 | − | 0.197947i | ||||
\(715\) | 4.41130 | − | 19.6482i | 0.164973 | − | 0.734802i | ||||
\(716\) | 53.1038 | 1.98458 | ||||||||
\(717\) | 7.67691 | 0.286699 | ||||||||
\(718\) | 43.4238 | 1.62056 | ||||||||
\(719\) | − | 3.27979i | − | 0.122316i | −0.998128 | − | 0.0611578i | \(-0.980521\pi\) | ||
0.998128 | − | 0.0611578i | \(-0.0194793\pi\) | |||||||
\(720\) | − | 9.24660i | − | 0.344601i | ||||||
\(721\) | 6.23549 | + | 34.1746i | 0.232222 | + | 1.27273i | ||||
\(722\) | − | 28.6657i | − | 1.06683i | ||||||
\(723\) | − | 13.6044i | − | 0.505955i | ||||||
\(724\) | 40.5505i | 1.50705i | ||||||||
\(725\) | 6.49479i | 0.241210i | ||||||||
\(726\) | 25.8828 | + | 12.2390i | 0.960599 | + | 0.454232i | ||||
\(727\) | 1.98302i | 0.0735461i | 0.999324 | + | 0.0367730i | \(0.0117079\pi\) | ||||
−0.999324 | + | 0.0367730i | \(0.988292\pi\) | |||||||
\(728\) | −20.8222 | − | 114.120i | −0.771724 | − | 4.22955i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 11.8031 | 0.436854 | ||||||||
\(731\) | 51.2614i | 1.89597i | ||||||||
\(732\) | − | 37.5471i | − | 1.38778i | ||||||
\(733\) | 1.56571 | 0.0578308 | 0.0289154 | − | 0.999582i | \(-0.490795\pi\) | ||||
0.0289154 | + | 0.999582i | \(0.490795\pi\) | |||||||
\(734\) | −73.4711 | −2.71187 | ||||||||
\(735\) | 6.54893 | − | 2.47214i | 0.241561 | − | 0.0911861i | ||||
\(736\) | 55.5747i | 2.04851i | ||||||||
\(737\) | 9.45968 | + | 2.12383i | 0.348452 | + | 0.0782323i | ||||
\(738\) | − | 21.7879i | − | 0.802025i | ||||||
\(739\) | − | 29.6758i | − | 1.09164i | −0.837902 | − | 0.545820i | \(-0.816218\pi\) | ||
0.837902 | − | 0.545820i | \(-0.183782\pi\) | |||||||
\(740\) | − | 12.7263i | − | 0.467829i | ||||||
\(741\) | 17.1587i | 0.630341i | ||||||||
\(742\) | 16.1992 | + | 88.7825i | 0.594693 | + | 3.25931i | ||||
\(743\) | − | 41.8830i | − | 1.53654i | −0.640127 | − | 0.768269i | \(-0.721118\pi\) | ||
0.640127 | − | 0.768269i | \(-0.278882\pi\) | |||||||
\(744\) | 19.2484i | 0.705682i | ||||||||
\(745\) | 16.8456 | 0.617173 | ||||||||
\(746\) | −25.7786 | −0.943820 | ||||||||
\(747\) | −9.31722 | −0.340899 | ||||||||
\(748\) | 66.1147 | + | 14.8437i | 2.41739 | + | 0.542738i | ||||
\(749\) | −4.79802 | − | 26.2963i | −0.175316 | − | 0.960847i | ||||
\(750\) | − | 2.60278i | − | 0.0950401i | ||||||
\(751\) | 1.81073 | 0.0660744 | 0.0330372 | − | 0.999454i | \(-0.489482\pi\) | ||||
0.0330372 | + | 0.999454i | \(0.489482\pi\) | |||||||
\(752\) | − | 117.113i | − | 4.27067i | ||||||
\(753\) | −21.9567 | −0.800148 | ||||||||
\(754\) | −102.638 | −3.73785 | ||||||||
\(755\) | 16.7907 | 0.611076 | ||||||||
\(756\) | 2.26741 | + | 12.4269i | 0.0824648 | + | 0.451962i | ||||
\(757\) | −39.7295 | −1.44399 | −0.721996 | − | 0.691897i | \(-0.756775\pi\) | ||||
−0.721996 | + | 0.691897i | \(0.756775\pi\) | |||||||
\(758\) | 67.0122i | 2.43399i | ||||||||
\(759\) | 4.19540 | − | 18.6866i | 0.152283 | − | 0.678279i | ||||
\(760\) | 20.4078 | 0.740269 | ||||||||
\(761\) | 33.5623 | 1.21663 | 0.608316 | − | 0.793695i | \(-0.291845\pi\) | ||||
0.608316 | + | 0.793695i | \(0.291845\pi\) | |||||||
\(762\) | − | 2.62924i | − | 0.0952473i | ||||||
\(763\) | −1.05222 | − | 5.76687i | −0.0380930 | − | 0.208775i | ||||
\(764\) | 119.930 | 4.33890 | ||||||||
\(765\) | 4.27913i | 0.154712i | ||||||||
\(766\) | −27.3602 | −0.988563 | ||||||||
\(767\) | − | 29.6966i | − | 1.07228i | ||||||
\(768\) | 18.7955i | 0.678226i | ||||||||
\(769\) | 16.3289 | 0.588835 | 0.294418 | − | 0.955677i | \(-0.404874\pi\) | ||||
0.294418 | + | 0.955677i | \(0.404874\pi\) | |||||||
\(770\) | 22.8207 | + | 0.921939i | 0.822401 | + | 0.0332244i | ||||
\(771\) | −3.99649 | −0.143930 | ||||||||
\(772\) | 24.8538i | 0.894507i | ||||||||
\(773\) | − | 18.0913i | − | 0.650699i | −0.945594 | − | 0.325349i | \(-0.894518\pi\) | ||
0.945594 | − | 0.325349i | \(-0.105482\pi\) | |||||||
\(774\) | −31.1798 | −1.12073 | ||||||||
\(775\) | 2.66550i | 0.0957475i | ||||||||
\(776\) | 17.6198 | 0.632514 | ||||||||
\(777\) | 1.26585 | + | 6.93771i | 0.0454122 | + | 0.248889i | ||||
\(778\) | 45.3951i | 1.62749i | ||||||||
\(779\) | 23.6569 | 0.847596 | ||||||||
\(780\) | 28.9888 | 1.03797 | ||||||||
\(781\) | −36.0421 | − | 8.09196i | −1.28969 | − | 0.289553i | ||||
\(782\) | − | 64.3139i | − | 2.29986i | ||||||
\(783\) | 6.49479 | 0.232105 | ||||||||
\(784\) | 60.5554 | − | 22.8589i | 2.16269 | − | 0.816388i | ||||
\(785\) | 5.04463 | 0.180050 | ||||||||
\(786\) | −52.9373 | −1.88821 | ||||||||
\(787\) | −5.83044 | −0.207833 | −0.103916 | − | 0.994586i | \(-0.533137\pi\) | ||||
−0.103916 | + | 0.994586i | \(0.533137\pi\) | |||||||
\(788\) | 67.3527i | 2.39934i | ||||||||
\(789\) | 10.4192 | 0.370934 | ||||||||
\(790\) | − | 19.3158i | − | 0.687226i | ||||||
\(791\) | 15.6365 | − | 2.85302i | 0.555968 | − | 0.101442i | ||||
\(792\) | −5.24660 | + | 23.3687i | −0.186430 | + | 0.830371i | ||||
\(793\) | 47.7482 | 1.69559 | ||||||||
\(794\) | −31.2487 | −1.10897 | ||||||||
\(795\) | −13.1055 | −0.464803 | ||||||||
\(796\) | − | 1.04054i | − | 0.0368809i | ||||||
\(797\) | − | 15.2515i | − | 0.540235i | −0.962827 | − | 0.270117i | \(-0.912938\pi\) | ||
0.962827 | − | 0.270117i | \(-0.0870625\pi\) | |||||||
\(798\) | −19.1449 | + | 3.49318i | −0.677724 | + | 0.123657i | ||||
\(799\) | 54.1973i | 1.91736i | ||||||||
\(800\) | − | 9.62422i | − | 0.340268i | ||||||
\(801\) | − | 0.418895i | − | 0.0148009i | ||||||
\(802\) | − | 37.9641i | − | 1.34056i | ||||||
\(803\) | −14.6750 | − | 3.29474i | −0.517869 | − | 0.116269i | ||||
\(804\) | 13.9567i | 0.492216i | ||||||||
\(805\) | −2.74231 | − | 15.0297i | −0.0966538 | − | 0.529726i | ||||
\(806\) | −42.1232 | −1.48373 | ||||||||
\(807\) | −22.2279 | −0.782459 | ||||||||
\(808\) | − | 44.4499i | − | 1.56374i | ||||||
\(809\) | 9.95650i | 0.350052i | 0.984564 | + | 0.175026i | \(0.0560009\pi\) | ||||
−0.984564 | + | 0.175026i | \(0.943999\pi\) | |||||||
\(810\) | −2.60278 | −0.0914524 | ||||||||
\(811\) | −42.0271 | −1.47577 | −0.737885 | − | 0.674927i | \(-0.764175\pi\) | ||||
−0.737885 | + | 0.674927i | \(0.764175\pi\) | |||||||
\(812\) | −14.7263 | − | 80.7100i | −0.516793 | − | 2.83237i | ||||
\(813\) | 4.55819i | 0.159863i | ||||||||
\(814\) | −5.04054 | + | 22.4509i | −0.176671 | + | 0.786903i | ||||
\(815\) | − | 16.9045i | − | 0.592139i | ||||||
\(816\) | 39.5674i | 1.38514i | ||||||||
\(817\) | − | 33.8543i | − | 1.18441i | ||||||
\(818\) | 22.1276i | 0.773672i | ||||||||
\(819\) | −15.8031 | + | 2.88344i | −0.552206 | + | 0.100755i | ||||
\(820\) | − | 39.9672i | − | 1.39571i | ||||||
\(821\) | 12.0729i | 0.421347i | 0.977556 | + | 0.210674i | \(0.0675657\pi\) | ||||
−0.977556 | + | 0.210674i | \(0.932434\pi\) | |||||||
\(822\) | −25.0761 | −0.874629 | ||||||||
\(823\) | 27.6005 | 0.962092 | 0.481046 | − | 0.876695i | \(-0.340257\pi\) | ||||
0.481046 | + | 0.876695i | \(0.340257\pi\) | |||||||
\(824\) | −94.8163 | −3.30308 | ||||||||
\(825\) | −0.726543 | + | 3.23607i | −0.0252950 | + | 0.112665i | ||||
\(826\) | 33.1341 | − | 6.04565i | 1.15288 | − | 0.210355i | ||||
\(827\) | 9.74038i | 0.338706i | 0.985555 | + | 0.169353i | \(0.0541678\pi\) | ||||
−0.985555 | + | 0.169353i | \(0.945832\pi\) | |||||||
\(828\) | 27.5700 | 0.958124 | ||||||||
\(829\) | 0.606700i | 0.0210716i | 0.999944 | + | 0.0105358i | \(0.00335370\pi\) | ||||
−0.999944 | + | 0.0105358i | \(0.996646\pi\) | |||||||
\(830\) | −24.2507 | −0.841754 | ||||||||
\(831\) | −18.0744 | −0.626995 | ||||||||
\(832\) | 39.8088 | 1.38012 | ||||||||
\(833\) | −28.0237 | + | 10.5786i | −0.970965 | + | 0.366526i | ||||
\(834\) | −8.02107 | −0.277747 | ||||||||
\(835\) | − | 6.32283i | − | 0.218811i | ||||||
\(836\) | −43.6638 | − | 9.80313i | −1.51014 | − | 0.339048i | ||||
\(837\) | 2.66550 | 0.0921331 | ||||||||
\(838\) | −63.6119 | −2.19744 | ||||||||
\(839\) | − | 43.5378i | − | 1.50309i | −0.659680 | − | 0.751546i | \(-0.729308\pi\) | ||
0.659680 | − | 0.751546i | \(-0.270692\pi\) | |||||||
\(840\) | 3.42943 | + | 18.7955i | 0.118327 | + | 0.648508i | ||||
\(841\) | −13.1823 | −0.454561 | ||||||||
\(842\) | − | 59.4768i | − | 2.04971i | ||||||
\(843\) | −12.7654 | −0.439662 | ||||||||
\(844\) | − | 126.710i | − | 4.36155i | ||||||
\(845\) | 23.8647i | 0.820972i | ||||||||
\(846\) | −32.9655 | −1.13338 | ||||||||
\(847\) | −28.1159 | − | 7.51645i | −0.966073 | − | 0.258268i | ||||
\(848\) | −121.181 | −4.16137 | ||||||||
\(849\) | 12.7384i | 0.437180i | ||||||||
\(850\) | 11.1376i | 0.382018i | ||||||||
\(851\) | 15.3918 | 0.527625 | ||||||||
\(852\) | − | 53.1763i | − | 1.82179i | ||||||
\(853\) | 8.69683 | 0.297774 | 0.148887 | − | 0.988854i | \(-0.452431\pi\) | ||||
0.148887 | + | 0.988854i | \(0.452431\pi\) | |||||||
\(854\) | 9.72061 | + | 53.2754i | 0.332632 | + | 1.82305i | ||||
\(855\) | − | 2.82604i | − | 0.0966487i | ||||||
\(856\) | 72.9583 | 2.49366 | ||||||||
\(857\) | 9.39456 | 0.320912 | 0.160456 | − | 0.987043i | \(-0.448704\pi\) | ||||
0.160456 | + | 0.987043i | \(0.448704\pi\) | |||||||
\(858\) | −51.1400 | − | 11.4816i | −1.74589 | − | 0.391977i | ||||
\(859\) | − | 18.3701i | − | 0.626779i | −0.949625 | − | 0.313389i | \(-0.898536\pi\) | ||
0.949625 | − | 0.313389i | \(-0.101464\pi\) | |||||||
\(860\) | −57.1953 | −1.95034 | ||||||||
\(861\) | 3.97542 | + | 21.7879i | 0.135482 | + | 0.742531i | ||||
\(862\) | 61.7549 | 2.10338 | ||||||||
\(863\) | 16.8723 | 0.574341 | 0.287171 | − | 0.957879i | \(-0.407285\pi\) | ||||
0.287171 | + | 0.957879i | \(0.407285\pi\) | |||||||
\(864\) | −9.62422 | −0.327423 | ||||||||
\(865\) | 8.78248i | 0.298613i | ||||||||
\(866\) | −73.2099 | −2.48777 | ||||||||
\(867\) | − | 1.31094i | − | 0.0445220i | ||||||
\(868\) | −6.04377 | − | 33.1239i | −0.205139 | − | 1.12430i | ||||
\(869\) | −5.39183 | + | 24.0156i | −0.182905 | + | 0.814672i | ||||
\(870\) | 16.9045 | 0.573116 | ||||||||
\(871\) | −17.7486 | −0.601389 | ||||||||
\(872\) | 16.0000 | 0.541828 | ||||||||
\(873\) | − | 2.43997i | − | 0.0825803i | ||||||
\(874\) | 42.4745i | 1.43672i | ||||||||
\(875\) | 0.474903 | + | 2.60278i | 0.0160546 | + | 0.0879900i | ||||
\(876\) | − | 21.6513i | − | 0.731531i | ||||||
\(877\) | 18.5832i | 0.627511i | 0.949504 | + | 0.313755i | \(0.101587\pi\) | ||||
−0.949504 | + | 0.313755i | \(0.898413\pi\) | |||||||
\(878\) | 43.6628i | 1.47355i | ||||||||
\(879\) | − | 14.0114i | − | 0.472593i | ||||||
\(880\) | −6.71805 | + | 29.9226i | −0.226465 | + | 1.00869i | ||||
\(881\) | − | 10.1366i | − | 0.341511i | −0.985313 | − | 0.170756i | \(-0.945379\pi\) | ||
0.985313 | − | 0.170756i | \(-0.0546209\pi\) | |||||||
\(882\) | −6.43443 | − | 17.0454i | −0.216658 | − | 0.573950i | ||||
\(883\) | −21.6343 | −0.728054 | −0.364027 | − | 0.931388i | \(-0.618598\pi\) | ||||
−0.364027 | + | 0.931388i | \(0.618598\pi\) | |||||||
\(884\) | −124.047 | −4.17215 | ||||||||
\(885\) | 4.89103i | 0.164410i | ||||||||
\(886\) | 29.1472i | 0.979218i | ||||||||
\(887\) | 17.5316 | 0.588653 | 0.294326 | − | 0.955705i | \(-0.404905\pi\) | ||||
0.294326 | + | 0.955705i | \(0.404905\pi\) | |||||||
\(888\) | −19.2484 | −0.645935 | ||||||||
\(889\) | 0.479730 | + | 2.62924i | 0.0160896 | + | 0.0881818i | ||||
\(890\) | − | 1.09029i | − | 0.0365467i | ||||||
\(891\) | 3.23607 | + | 0.726543i | 0.108412 | + | 0.0243401i | ||||
\(892\) | − | 9.39534i | − | 0.314579i | ||||||
\(893\) | − | 35.7933i | − | 1.19778i | ||||||
\(894\) | − | 43.8453i | − | 1.46641i | ||||||
\(895\) | − | 11.1224i | − | 0.371782i | ||||||
\(896\) | −1.03682 | − | 5.68248i | −0.0346379 | − | 0.189838i | ||||
\(897\) | 35.0605i | 1.17063i | ||||||||
\(898\) | 19.4899i | 0.650386i | ||||||||
\(899\) | −17.3118 | −0.577382 | ||||||||
\(900\) | −4.77447 | −0.159149 | ||||||||
\(901\) | 56.0800 | 1.86829 | ||||||||
\(902\) | −15.8299 | + | 70.5073i | −0.527077 | + | 2.34764i | ||||
\(903\) | 31.1798 | − | 5.68906i | 1.03760 | − | 0.189320i | ||||
\(904\) | 43.3828i | 1.44289i | ||||||||
\(905\) | 8.49321 | 0.282324 | ||||||||
\(906\) | − | 43.7025i | − | 1.45192i | ||||||
\(907\) | 25.4469 | 0.844949 | 0.422475 | − | 0.906375i | \(-0.361162\pi\) | ||||
0.422475 | + | 0.906375i | \(0.361162\pi\) | |||||||
\(908\) | −7.66432 | −0.254349 | ||||||||
\(909\) | −6.15537 | −0.204161 | ||||||||
\(910\) | −41.1321 | + | 7.50495i | −1.36352 | + | 0.248787i | ||||
\(911\) | 16.7205 | 0.553973 | 0.276987 | − | 0.960874i | \(-0.410664\pi\) | ||||
0.276987 | + | 0.960874i | \(0.410664\pi\) | |||||||
\(912\) | − | 26.1313i | − | 0.865294i | ||||||
\(913\) | 30.1512 | + | 6.76936i | 0.997858 | + | 0.224033i | ||||
\(914\) | −92.1873 | −3.04928 | ||||||||
\(915\) | −7.86414 | −0.259980 | ||||||||
\(916\) | − | 43.2195i | − | 1.42801i | ||||||
\(917\) | 52.9373 | − | 9.65892i | 1.74814 | − | 0.318966i | ||||
\(918\) | 11.1376 | 0.367597 | ||||||||
\(919\) | − | 3.01777i | − | 0.0995469i | −0.998761 | − | 0.0497734i | \(-0.984150\pi\) | ||
0.998761 | − | 0.0497734i | \(-0.0158499\pi\) | |||||||
\(920\) | 41.6993 | 1.37479 | ||||||||
\(921\) | 8.27920i | 0.272809i | ||||||||
\(922\) | − | 9.90961i | − | 0.326356i | ||||||
\(923\) | 67.6236 | 2.22586 | ||||||||
\(924\) | 1.69118 | − | 41.8616i | 0.0556357 | − | 1.37715i | ||||
\(925\) | −2.66550 | −0.0876410 | ||||||||
\(926\) | − | 50.5367i | − | 1.66074i | ||||||
\(927\) | 13.1300i | 0.431247i | ||||||||
\(928\) | 62.5073 | 2.05190 | ||||||||
\(929\) | 44.3174i | 1.45401i | 0.686634 | + | 0.727004i | \(0.259088\pi\) | ||||
−0.686634 | + | 0.727004i | \(0.740912\pi\) | |||||||
\(930\) | 6.93771 | 0.227496 | ||||||||
\(931\) | 18.5076 | − | 6.98636i | 0.606561 | − | 0.228969i | ||||
\(932\) | 35.3937i | 1.15936i | ||||||||
\(933\) | −11.0297 | −0.361096 | ||||||||
\(934\) | −81.0506 | −2.65206 | ||||||||
\(935\) | 3.10897 | − | 13.8476i | 0.101674 | − | 0.452863i | ||||
\(936\) | − | 43.8453i | − | 1.43313i | ||||||
\(937\) | −55.4748 | −1.81228 | −0.906142 | − | 0.422974i | \(-0.860986\pi\) | ||||
−0.906142 | + | 0.422974i | \(0.860986\pi\) | |||||||
\(938\) | −3.61328 | − | 19.8031i | −0.117978 | − | 0.646595i | ||||
\(939\) | 7.27776 | 0.237501 | ||||||||
\(940\) | −60.4710 | −1.97235 | ||||||||
\(941\) | −56.3860 | −1.83813 | −0.919065 | − | 0.394106i | \(-0.871054\pi\) | ||||
−0.919065 | + | 0.394106i | \(0.871054\pi\) | |||||||
\(942\) | − | 13.1301i | − | 0.427800i | ||||||
\(943\) | 48.3382 | 1.57411 | ||||||||
\(944\) | 45.2254i | 1.47196i | ||||||||
\(945\) | 2.60278 | − | 0.474903i | 0.0846685 | − | 0.0154486i | ||||
\(946\) | 100.900 | + | 22.6534i | 3.28054 | + | 0.736527i | ||||
\(947\) | −26.7831 | −0.870333 | −0.435167 | − | 0.900350i | \(-0.643311\pi\) | ||||
−0.435167 | + | 0.900350i | \(0.643311\pi\) | |||||||
\(948\) | −35.4324 | −1.15079 | ||||||||
\(949\) | 27.5337 | 0.893783 | ||||||||
\(950\) | − | 7.35557i | − | 0.238646i | ||||||
\(951\) | − | 8.69007i | − | 0.281795i | ||||||
\(952\) | −14.6750 | − | 80.4285i | −0.475619 | − | 2.60670i | ||||
\(953\) | 26.0197i | 0.842861i | 0.906861 | + | 0.421431i | \(0.138472\pi\) | ||||
−0.906861 | + | 0.421431i | \(0.861528\pi\) | |||||||
\(954\) | 34.1106i | 1.10437i | ||||||||
\(955\) | − | 25.1189i | − | 0.812830i | ||||||
\(956\) | − | 36.6531i | − | 1.18545i | ||||||
\(957\) | −21.0176 | − | 4.71874i | −0.679402 | − | 0.152535i | ||||
\(958\) | − | 107.733i | − | 3.48069i | ||||||
\(959\) | 25.0761 | − | 4.57538i | 0.809749 | − | 0.147747i | ||||
\(960\) | −6.55653 | −0.211611 | ||||||||
\(961\) | 23.8951 | 0.770810 | ||||||||
\(962\) | − | 42.1232i | − | 1.35811i | ||||||
\(963\) | − | 10.1032i | − | 0.325570i | ||||||
\(964\) | −64.9540 | −2.09203 | ||||||||
\(965\) | 5.20556 | 0.167573 | ||||||||
\(966\) | −39.1189 | + | 7.13763i | −1.25863 | + | 0.229650i | ||||
\(967\) | 22.6715i | 0.729066i | 0.931190 | + | 0.364533i | \(0.118771\pi\) | ||||
−0.931190 | + | 0.364533i | \(0.881229\pi\) | |||||||
\(968\) | 33.9567 | − | 71.8109i | 1.09141 | − | 2.30809i | ||||
\(969\) | 12.0930i | 0.388483i | ||||||||
\(970\) | − | 6.35069i | − | 0.203909i | ||||||
\(971\) | − | 16.5616i | − | 0.531488i | −0.964044 | − | 0.265744i | \(-0.914382\pi\) | ||
0.964044 | − | 0.265744i | \(-0.0856176\pi\) | |||||||
\(972\) | 4.77447i | 0.153141i | ||||||||
\(973\) | 8.02107 | − | 1.46352i | 0.257144 | − | 0.0469184i | ||||
\(974\) | 81.8797i | 2.62359i | ||||||||
\(975\) | − | 6.07163i | − | 0.194448i | ||||||
\(976\) | −72.7166 | −2.32760 | ||||||||
\(977\) | 2.81501 | 0.0900600 | 0.0450300 | − | 0.998986i | \(-0.485662\pi\) | ||||
0.0450300 | + | 0.998986i | \(0.485662\pi\) | |||||||
\(978\) | −43.9987 | −1.40692 | ||||||||
\(979\) | −0.304345 | + | 1.35557i | −0.00972691 | + | 0.0433243i | ||||
\(980\) | −11.8031 | − | 31.2677i | −0.377037 | − | 0.998809i | ||||
\(981\) | − | 2.21566i | − | 0.0707405i | ||||||
\(982\) | 37.1906 | 1.18680 | ||||||||
\(983\) | − | 53.1572i | − | 1.69545i | −0.530434 | − | 0.847726i | \(-0.677971\pi\) | ||
0.530434 | − | 0.847726i | \(-0.322029\pi\) | |||||||
\(984\) | −60.4499 | −1.92707 | ||||||||
\(985\) | 14.1068 | 0.449481 | ||||||||
\(986\) | −72.3366 | −2.30367 | ||||||||
\(987\) | 32.9655 | − | 6.01488i | 1.04930 | − | 0.191456i | ||||
\(988\) | 81.9237 | 2.60634 | ||||||||
\(989\) | − | 69.1747i | − | 2.19963i | ||||||
\(990\) | 8.42278 | + | 1.89103i | 0.267693 | + | 0.0601009i | ||||
\(991\) | 3.92919 | 0.124815 | 0.0624075 | − | 0.998051i | \(-0.480122\pi\) | ||||
0.0624075 | + | 0.998051i | \(0.480122\pi\) | |||||||
\(992\) | 25.6533 | 0.814494 | ||||||||
\(993\) | − | 17.2380i | − | 0.547031i | ||||||
\(994\) | 13.7669 | + | 75.4515i | 0.436659 | + | 2.39318i | ||||
\(995\) | −0.217938 | −0.00690911 | ||||||||
\(996\) | 44.4848i | 1.40955i | ||||||||
\(997\) | 8.49429 | 0.269017 | 0.134508 | − | 0.990912i | \(-0.457054\pi\) | ||||
0.134508 | + | 0.990912i | \(0.457054\pi\) | |||||||
\(998\) | 44.1768i | 1.39839i | ||||||||
\(999\) | 2.66550i | 0.0843326i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1155.2.i.c.76.15 | yes | 16 | |
7.6 | odd | 2 | inner | 1155.2.i.c.76.16 | yes | 16 | |
11.10 | odd | 2 | inner | 1155.2.i.c.76.1 | ✓ | 16 | |
77.76 | even | 2 | inner | 1155.2.i.c.76.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.i.c.76.1 | ✓ | 16 | 11.10 | odd | 2 | inner | |
1155.2.i.c.76.2 | yes | 16 | 77.76 | even | 2 | inner | |
1155.2.i.c.76.15 | yes | 16 | 1.1 | even | 1 | trivial | |
1155.2.i.c.76.16 | yes | 16 | 7.6 | odd | 2 | inner |